How can I retrieve deleted messages

If you were using iCloud syncing for messages, once a message is deleted from a device, it's deleted from all connected devices. There are no backups.

If you were not using iCloud syncing and you have a backup that contains the messages, you can restore the phone to that back up.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Note that restoring the phone to a back up will overwrite everything currently on the phone.

You lost some messages or texts

If “Messages” was turned ON in Settings, your name, iCloud then no you cannot retrieve them.

If “Messages” was turned OFF in Settings, your name, iCloud then you can restore the entire most recent backup and lose everything else since that date. Without a daily iCloud backup that is probably not feasible.

In other words almost impossible